Quark matter meets cold atoms

474th International Wilhelm und Else Heraeus Seminar on

Strong interactions: from methods to structures, Bad Honnef, Feb 12-16, 2011

Mei Huang IHEP, CAS

TPCSF, CAS

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Content

I. Recent progress of QCD phase structure

Cold quark matter & cold atoms

II. Interplay between chiral and

deconfinement phase transitions

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I. Recent Progress of QCD phase structure

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QCD phase diagram: 1974 ---- 1999

For physical quark mass, crossover at zero and small baryon density, and first order phase transition at finite baryon density. CEP is the end point of first order phase transition.

HM

QGP

CEP

Heating QCD vacuum: (RHIC, LHC, early universe)

1, Chiral symmetry restoration

2, Deconfinement phase transition

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QCD phase diagram after 1999

Squeezing QCD matter: Color superconductor

HM

QGP

CSC

Pairing with mismatch beta-equilibrium,

charge neutrality

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Imbalanced CSC meets imbalanced cold atoms

MH, I.Shovkovy, PRD70:051501,2004; 094030,2004

Shovkovy, M.H, PLB564:205,2003M.H., I. Shovkovy, NPA729:835,2003

Interior gap & Breached Pairing

Liu,Wilczek, PRL90:047002,2003Gubankova, Liu, Wilczek, PRL91:032001,2003

Gapless 2SC phase

Chromomagnetic instability Superfluid density is negative

Wu, Yip, PRA67: 053603, 2003

Other possibilities: LOFF state(1964), phase separation

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Zwierlein, Schirotzek, Schunck, & Ketterle, Science 2005, cond-mat/0511197Partridge, Li, Kamar, Liao, & Hulet, Science 2005, cond-mat/0511752.

n1=n2

n1>>n2

phase separation

Imbalanced pairing in cold atom system

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M.H. PRD73:045007, 2006; Int.J.Mod.Phys.A21, 910, (2006)

I. Giannakis, D.F.Hou, M.H., H.C.Ren, PRD75:011501,2007, PRD75:014015,2007

Group G

Subspace: Group H

Coset space: M=G/H

Instability of NG bosons FF-like stateHiggs instability spatial inhomogeneity

For gapless superfluidity (BP) state, no charge Coulomb energycompetes with Higgs instability, phase separation is more favored.

9Abuki-Baym-Hatsuda-Yamamoto, arXiv:1003.0408

BCS-BEC crossover

Abuki,

He, Zhuang,

Deng, Pu, Wang

Abuki-Baym-Hatsuda-Yamamoto ……

10Compact Star

sQGP

QCD phase diagram High T part after 2003

P. Romatschke, U. Romatschke, Phys.Rev.Lett.99:172301,2007

Discovery of sQGP at RHIC

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Viscosity/entropy density (units of ) Bk/

He near point

QGP simulations

String theory limit

Slide from John E. Thomas

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II. Interplay between chiral and deconfinement phase transitions

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2007: Quarkyonic phase chiral symmetric but confined phase

L. McLerran, R. Pisarski 2007

Phase diagram at large Nc Conditions:• Large Nc• Deconfined quark Fermi surface

Particle-particle pairing is suppressed

Particle-hole (color singlet) pairing dominant

chiral density wave

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Can “Quarkyonic phase” be realized in real QCD?

Fukushima, Hatsuda, arXiv:1005.4814

“Quarkyonic phase” has extended meaning, here indicates chiral symmetric but confined phase.

More interests are attracted to the relation between

chiral and deconfinement phase transitions

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Lattice results on chiral and deconfinement phase transitions at zero mu

Chiral limit: coincide

Physical quark mass (2+1):

RBC-Bielefeld: coincide

Wuppertal-Budapest: (crossover feature)

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Relation between chiral and deconfinement phase transitions in PNJL or PLSM model

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Order parameter of center symmetry: Polyakov loop

Confinement: center symmetry

Deconfinement:

center symmetry breaking

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Relation between chiral and deconfinement phase transitions in PNJL model

Different choices of Polyakov potential: fixed by lattice QCD at finite T

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Sasaki,Friman,Redlich, hep-ph/0611147

Kenji Fukushima, arXiv:0803.3318

Chiral symmetry broken and deconfined / coincidence

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Chiral symmetric but confined phase in PLSM model

H. Mao, J. Jin, MH, arXiv:0906.1324, J.Phys.G37:035001,2010

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In PNJL or PLSM model, at zero baryon density, whether chiral phase transition and deconfinement phase transition coincide or not depends much on parameters used.

In these models, there are no real interplay between chiral phase transition and deconfinement phase transition.

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Dressed Polyakov loop

An equivalent order parameter for deconfinement phase transition:

Gattringer,PRL97(2006)032003Bilgici et.al. PRD77(2008)094007Braun, Hass,Marhauser,Pawlowski, arXiv:0908.0008

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Order parameter of center symmetry:

Dressed Polyakov loop or dual chiral condensateGattringer,PRL97(2006)032003

n=1: dressed Polyakov loop

Dressed Polyakov on lattice: Bilgici et.al. in DSE: Fischer et.al.

Linking confinement to spectral properties of Dirac operator

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The periodicity property of the quark fields change under the the gauge transformation Uz:

Dual observables:

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Dressed Polyakov loop in NJL model

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Chiral limit: coincide

T.Mukherjee, H.Chen, M.Huang, arXiv:1005.2482,PRD82:034015,2010

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Physical quark mass:

crossover region

T.Mukherjee, H.Chen, M.Huang, arXiv:1005.2482,PRD82:034015,2010

Y.Aoki, Z.Fofor,A.Katz,K.Szabo,hep-lat/0609068, PLB643:46-54,2006

1st order:

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Why for 1st phase transition?

T.Mukherjee, H.Chen, M.Huang, arXiv:1005.2482,PRD82:034015,2010

for 1st phase transitionis preserved by the singularity.

If this is true, there will be no “quarkyonic” phase or chiral symmetric but confined phaseat finite density.

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Nf=2+1 NJL model: sequential (flavor dependent) phase transitions

Fukun Xu, T.Mukherjee, M.H., arXiv:1101.2952

CEP related to future RHIC and FAIR Exp. will be the CEP of light u,d quarks

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Summary

1, Much progress on QCD phase diagram at finite temperature and density has been made in the last 10 years.

2, Quantitative results are still few!